<!-------- @HEADER
 !
 ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 !
 !  Zoltan Toolkit for Load-balancing, Partitioning, Ordering and Coloring
 !                  Copyright 2012 Sandia Corporation
 !
 ! Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
 ! the U.S. Government retains certain rights in this software.
 !
 ! Redistribution and use in source and binary forms, with or without
 ! modification, are permitted provided that the following conditions are
 ! met:
 !
 ! 1. Redistributions of source code must retain the above copyright
 ! notice, this list of conditions and the following disclaimer.
 !
 ! 2. Redistributions in binary form must reproduce the above copyright
 ! notice, this list of conditions and the following disclaimer in the
 ! documentation and/or other materials provided with the distribution.
 !
 ! 3. Neither the name of the Corporation nor the names of the
 ! contributors may be used to endorse or promote products derived from
 ! this software without specific prior written permission.
 !
 ! THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
 ! EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 ! IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 ! PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE
 ! CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
 ! EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
 ! PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
 ! PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
 ! LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
 ! NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 ! SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 !
 ! Questions? Contact Karen Devine	kddevin@sandia.gov
 !                    Erik Boman	egboman@sandia.gov
 !
 ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 !
 ! @HEADER
-------> 
<!doctype html public "-//w3c//dtd html 4.0 transitional//en">
<html>
<head>
   <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
   <meta name="GENERATOR" content="Mozilla/4.76 [en] (X11; U; Linux 2.4.2-2smp i686) [Netscape]">
  <meta name="sandia.approval_type" content="formal">
  <meta name="sandia.approved" content="SAND2007-4748W">
  <meta name="author" content="Zoltan PI">

   <title>Zoltan User's Guide:  Ordering Interface</title>
</head>
<body bgcolor="#FFFFFF">

<div align=right><b><i><a href="ug.html">Zoltan User's Guide</a>&nbsp;
|&nbsp; <a href="ug_interface_color.html">Next</a>&nbsp; |&nbsp; <a href="ug_interface_mig.html">Previous</a></i></b></div>

<h2>
<a NAME="Ordering Functions"></a>Ordering Functions</h2>
Zoltan provides functions for ordering a set of objects, 
typically given as a graph (which may correspond to a sparse matrix).
The following functions are the ordering interface functions in Zoltan.
The first is the main function, and the others are accessor functions
that should only be called after <a href="#Zoltan_Order">Zoltan_Order</a>.
<blockquote>
<ul>
<li>
<li><b><a href="#Zoltan_Order">Zoltan_Order</a></b></li>
<li><b><a href="#Zoltan_Order_Get_Num_Blocks">Zoltan_Order_Get_Num_Blocks</a></b></li>
<li><b><a href="#Zoltan_Order_Get_Block_Bounds">Zoltan_Order_Get_Block_Bounds</a></b></li>
<li><b><a href="#Zoltan_Order_Get_Block_Size">Zoltan_Order_Get_Block_Size</a></b></li>
<li><b><a href="#Zoltan_Order_Get_Block_Parent">Zoltan_Order_Get_Block_Parent</a></b></li>
<li><b><a href="#Zoltan_Order_Get_Num_Leaves">Zoltan_Order_Get_Num_Leaves</a></b></li>
<li><b><a href="#Zoltan_Order_Get_Block_Leaves">Zoltan_Order_Get_Block_Leaves</a></b></li>
</ul>
</blockquote>
<!------------------------------------------------------------------------->
<hr WIDTH="100%"><a NAME="Zoltan_Order"></a>
<hr WIDTH="100%">
<table WIDTH="100%" NOSAVE >
<tr NOSAVE>
<td VALIGN=TOP NOSAVE>C:</td>

<td WIDTH="85%">int <b>Zoltan_Order</b> (
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;struct <b>Zoltan_Struct</b> *<i>zz</i>,
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;int <i>num_gid_entries</i>, 
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;int <i>num_obj</i>,
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<b><a href="ug_usage.html#Data Types for Object IDs">ZOLTAN_ID_PTR </a></b><i>global_ids</i>,
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<b><a href="ug_usage.html#Data Types for Object IDs">ZOLTAN_ID_PTR </a></b> <i>rank</i>, 
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;)
</td>
</tr>

<tr NOSAVE>
<td VALIGN=TOP WIDTH="15%" NOSAVE>FORTRAN:</td>

<td>FUNCTION <b>Zoltan_Order</b>(<i>zz, num_gid_entries</i>,
<i>num_obj, global_ids</i>, <i>rank, iperm</i>)
<br>INTEGER(Zoltan_INT) :: Zoltan_Order
<br>TYPE(Zoltan_Struct), INTENT(IN) :: zz
<br>INTEGER(Zoltan_INT), INTENT(IN) :: num_gid_entries
<br>INTEGER(Zoltan_INT), INTENT(IN) :: num_obj
<br>INTEGER(Zoltan_INT) :: global_ids(*)
<br>INTEGER(Zoltan_INT) :: rank(*)
</tr>

<tr NOSAVE>
<td VALIGN=TOP NOSAVE>C++:</td>

<td WIDTH="85%">int <b>Zoltan::Order</b> (
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;int <i>num_gid_entries</i>, 
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;int <i>num_obj</i>,
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<b><a href="ug_usage.html#Data Types for Object IDs">ZOLTAN_ID_PTR </a></b><i>global_ids</i>,
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<b><a href="ug_usage.html#Data Types for Object IDs">ZOLTAN_ID_PTR </a></b> <i>rank</i>, 
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;)
</td>
</tr>
</table>

<hr WIDTH="100%"><b>Zoltan_Order </b>invokes the ordering routine specified
by the&nbsp; <i><a href="ug_order.html#ORDER_METHOD">ORDER_METHOD</a></i> parameter.
Results of the ordering is returned in the array <i>rank </i>.
<p>
<li>
<i>rank[i]</i>
gives the rank of <i>global_ids[i] </i>in the computed ordering, which is a number between 0 and N-1 where N is the overall number of objects across all the processors. (Note: This will change in future versions. A permuted set of GIDs will be returned instead.)
</li>
 The arrays
<i>global_ids, rank,</i>
should all be allocated by the application before
<b>Zoltan_Order</b> is
called. Each array must have space for (at least)
<i>num_obj </i>elements,
where <i>num_obj </i>is the number of objects the user want to know informations about.
<br>&nbsp;
<table WIDTH="100%" NOSAVE >
<tr>
<td VALIGN=TOP WIDTH="20%"><b>Arguments:</b></td>

<td WIDTH="80%"></td>
</tr>

<tr>
<td VALIGN=TOP><i>&nbsp;&nbsp;&nbsp; zz</i></td>

<td>Pointer to the Zoltan structure, created by <b><a href="ug_interface_init.html#Zoltan_Create">Zoltan_Create</a></b>,
to be used in this invocation of the load-balancing routine.</td>
</tr>

<tr NOSAVE>
<td VALIGN=TOP NOSAVE>&nbsp;&nbsp;&nbsp; <i>num_gid_entries</i></td>

<td>Input: the number of array entries used to describe a single
global ID.&nbsp; This value is the maximum value over all processors of
the parameter <a href="ug_param.html#NUM_GID_ENTRIES">NUM_GID_ENTRIES</a>.</td>
</tr>


<tr VALIGN=TOP NOSAVE>
<td>&nbsp;&nbsp;&nbsp; <i>num_obj</i></td>

<td NOSAVE>Number of objects for which we want to know the ordering. Objects may be non-local.</td>
</tr>

<tr>
<td VALIGN=TOP><i>&nbsp;&nbsp;&nbsp; global_ids</i></td>

<td>An array of global IDs of objects for which we want to know the
ordering on this processor. Size of this array must be <i>num_obj</i>.
<br>Objects may be non-local. Objects IDs may be repeated on several
processor.</td> </tr>


<tr>
<td VALIGN=TOP><i>&nbsp;&nbsp;&nbsp; rank</i></td>

<td>Upon return, an array of length <i>num_obj </i>containing the rank
of each object in the computed ordering. When rank[i] = j, that means that
the object corresponding to
<i>global_ids[i]
</i>is the<i> j</i>th object
in the ordering. (This array corresponds directly to the <i>perm </i>array
in METIS and the <i>order</i> array in ParMETIS.) Note that the rank may
refer to either a local or a global ordering, depending on <a href="ug_order.html#ORDER_TYPE">ORDER_TYPE</a>.&nbsp;
Memory for this array must have been allocated before <b>Zoltan_Order</b> is
called.</td>
</tr>

<tr>
<td><b>Returned Value:</b></td>

<td></td>
</tr>

<tr>
<td VALIGN=TOP>&nbsp;&nbsp;&nbsp; int</td>

<td><a href="ug_interface.html#Error Codes">Error code</a>.</td>
</tr>
</table>

<p>

<!------------------------------------------------------------------------->

<hr WIDTH="100%">


<h3>Accessors</h3>

Zoltan primarily supports nested dissection orderings, which are
typically used to reduce fill in direct solvers. For this use case, it is 
important to get additional information (the separators).
The accessor functions below define the Zoltan interface.
Note that these functions should be called after 
<a href="#Zoltan_Order">Zoltan_Order</a>.

<!------------------------------------------------------------------------->
<a NAME="Zoltan_Order_Get_Num_Blocks"></a>
<hr WIDTH="100%">
<table WIDTH="100%" NOSAVE >
<tr NOSAVE>
<td VALIGN=TOP NOSAVE>C:</td>

<td WIDTH="85%">int <b>Zoltan_Order_Get_Num_Blocks</b> (
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;struct <b>Zoltan_Struct</b> *<i>zz</i>)
</tr>

<tr NOSAVE>
<td VALIGN=TOP NOSAVE>C++:</td>

<td WIDTH="85%">int <b>Zoltan::Order_Get_Num_Blocks</b> ()
</tr>

</table>

<hr WIDTH="100%"><b>Zoltan_Order_Get_Num_Blocks </b> returns the number of subdomains (or column blocks) computed during the ordering. For a Nested Dissection based ordering method, it corresponds to the sum of the separators and the subgraphs of the lowest level. For example, after one bisection the number of blocks is three.
<br>&nbsp;
<table WIDTH="100%" NOSAVE >
<tr>
<td VALIGN=TOP WIDTH="20%"><b>Arguments:</b></td>

<td WIDTH="80%"></td>
</tr>

<tr>
<td VALIGN=TOP><i>&nbsp;&nbsp;&nbsp; zz</i></td>

<td>Pointer to the Zoltan structure, created by <b><a href="ug_interface_init.html#Zoltan_Create">Zoltan_Create</a></b>,
which has been used in the ordering routine.</td>
</tr>

<tr>
<td><b>Returned Value:</b></td>

<td></td>
</tr>

<tr>
<td VALIGN=TOP>&nbsp;&nbsp;&nbsp; int</td>

<td>The number of <i>blocks</i> (subdomains).</td>
</tr>
</table>

<p>

<!------------------------------------------------------------------------->

<!------------------------------------------------------------------------->
<hr WIDTH="100%"><a NAME="Zoltan_Order_Get_Block_Bounds"></a>
<hr WIDTH="100%">
<table WIDTH="100%" NOSAVE >
<tr NOSAVE>
<td VALIGN=TOP NOSAVE>C:</td>

<td WIDTH="85%">int <b>Zoltan_Order_Get_Block_Bounds</b> (
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;struct <b>Zoltan_Struct</b> *<i>zz</i>,
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;int <i>block_id</i>,
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;int *<i>first</i>,
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;int *<i>last</i>)
</tr>


<tr NOSAVE>
<td VALIGN=TOP NOSAVE>C++:</td>

<td WIDTH="85%">int <b>Zoltan::Order_Get_Block_Bounds</b> (
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;int <i>block_id</i>,
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;int &<i>first</i>,
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;int &<i>last</i>)
</tr>

</table>

<hr WIDTH="100%"><b>Zoltan_Order_Get_Block_Bounds </b> gives the
boundaries of the given block. The <i>first</i> and <i>last</i>
parameters contain upon return the indices of the begin and the end of
the block. These indices are from the global continuous numbering
between 1 and N-1 of the N distributed objects.

<br>&nbsp;

  <table WIDTH="100%" NOSAVE > <tr> <td VALIGN=TOP
WIDTH="20%"><b>Arguments:</b></td>

<td WIDTH="80%"></td>
</tr>

<tr>
<td VALIGN=TOP><i>&nbsp;&nbsp;&nbsp; zz</i></td>

<td>Pointer to the Zoltan structure, created by <b><a href="ug_interface_init.html#Zoltan_Create">Zoltan_Create</a></b>,
which has been used in the ordering routine.</td>
</tr>

<tr>
<td VALIGN=TOP><i>&nbsp;&nbsp;&nbsp; block_id</i></td>

<td>The number of the block we want informations on.</td>
</tr>


<tr>
<td VALIGN=TOP><i>&nbsp;&nbsp;&nbsp; first</i></td>

<td>Upon return, pointer to the value of the begining of the block.</td>
</tr>

<tr>
<td VALIGN=TOP><i>&nbsp;&nbsp;&nbsp; last</i></td>

<td>Upon return, pointer to the value of the end of the block.</td>
</tr>


<tr>
<td><b>Returned Value:</b></td>

<td></td>
</tr>

<tr>
<td VALIGN=TOP>&nbsp;&nbsp;&nbsp; int</td>

<td><a href="ug_interface.html#Error Codes">Error code</a>.</td>
</tr>
</table>

<p>

<!------------------------------------------------------------------------->

<!------------------------------------------------------------------------->
<hr WIDTH="100%"><a NAME="Zoltan_Order_Get_Block_Size"></a>
<hr WIDTH="100%">
<table WIDTH="100%" NOSAVE >
<tr NOSAVE>
<td VALIGN=TOP NOSAVE>C:</td>

<td WIDTH="85%">int <b>Zoltan_Order_Get_Block_Size</b> (
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;struct <b>Zoltan_Struct</b> *<i>zz</i>,
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;int <i>block_id</i>)
</tr>


<tr NOSAVE>
<td VALIGN=TOP NOSAVE>C++:</td>

<td WIDTH="85%">int <b>Zoltan::Order_Get_Block_Size</b> (
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;int <i>block_id</i>)
</tr>

</table>

<hr WIDTH="100%"><b>Zoltan_Order_Get_Block_Size </b> returns the number of objects in the block <i>block_id</i>.
<br>&nbsp;
<table WIDTH="100%" NOSAVE >
<tr>
<td VALIGN=TOP WIDTH="20%"><b>Arguments:</b></td>

<td WIDTH="80%"></td>
</tr>

<tr>
<td VALIGN=TOP><i>&nbsp;&nbsp;&nbsp; zz</i></td>

<td>Pointer to the Zoltan structure, created by <b><a href="ug_interface_init.html#Zoltan_Create">Zoltan_Create</a></b>,
which has been used in the ordering routine.</td>
</tr>

<tr>
<td VALIGN=TOP><i>&nbsp;&nbsp;&nbsp; block_id</i></td>

<td>The indice of the block we want to know the size.</tr>

<tr>
<td><b>Returned Value:</b></td>

<td></td>
</tr>

<tr>
<td VALIGN=TOP>&nbsp;&nbsp;&nbsp; int</td>

<td>The number of objects in this given <i>block</i>.</td>
</tr>
</table>

<p>

<!------------------------------------------------------------------------->

<!------------------------------------------------------------------------->
<hr WIDTH="100%"><a NAME="Zoltan_Order_Get_Block_Parent"></a>
<hr WIDTH="100%">
<table WIDTH="100%" NOSAVE >
<tr NOSAVE>
<td VALIGN=TOP NOSAVE>C:</td>

<td WIDTH="85%">int <b>Zoltan_Order_Get_Block_Parent</b> (
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;struct <b>Zoltan_Struct</b> *<i>zz</i>,
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;int <i>block_id</i>)
</tr>

<tr NOSAVE>
<td VALIGN=TOP NOSAVE>C++:</td>

<td WIDTH="85%">int <b>Zoltan::Order_Get_Block_Parent</b> (
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;int <i>block_id</i>)
</tr>

</table>

<hr WIDTH="100%"><b>Zoltan_Order_Get_Block_Parent </b> returns the
number (id) of the parent block in the elimination tree. The value is
-1 for the root of the tree.

<br>&nbsp;
<table WIDTH="100%" NOSAVE >
<tr>
<td VALIGN=TOP WIDTH="20%"><b>Arguments:</b></td>

<td WIDTH="80%"></td>
</tr>

<tr>
<td VALIGN=TOP><i>&nbsp;&nbsp;&nbsp; zz</i></td>

<td>Pointer to the Zoltan structure, created by <b><a href="ug_interface_init.html#Zoltan_Create">Zoltan_Create</a></b>,
which has been used in the ordering routine.</td>
</tr>

<tr>
<td VALIGN=TOP><i>&nbsp;&nbsp;&nbsp; block_id</i></td>

<td>The indice of the block we want to know the size.</tr>

<tr>
<td><b>Returned Value:</b></td>

<td></td>
</tr>

<tr>
<td VALIGN=TOP>&nbsp;&nbsp;&nbsp; int</td>

<td>The number (id) of the parent block in the elimination tree. The
value is -1 for the root of the tree.</td> </tr> </table>

<p>

<!------------------------------------------------------------------------->

<!------------------------------------------------------------------------->
<hr WIDTH="100%"><a NAME="Zoltan_Order_Get_Num_Leaves"></a>
<hr WIDTH="100%">
<table WIDTH="100%" NOSAVE >
<tr NOSAVE>
<td VALIGN=TOP NOSAVE>C:</td>

<td WIDTH="85%">int <b>Zoltan_Order_Get_Num_Leaves</b> (
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;struct <b>Zoltan_Struct</b> *<i>zz</i>)
</tr>

<tr NOSAVE>
<td VALIGN=TOP NOSAVE>C++:</td>

<td WIDTH="85%">int <b>Zoltan::Order_Get_Num_Leaves</b> ()
</tr>

</table>

<hr WIDTH="100%"><b>Zoltan_Order_Get_Num_Leaves </b> returns the number of leaves in the elimination tree.
<br>&nbsp;
<table WIDTH="100%" NOSAVE >
<tr>
<td VALIGN=TOP WIDTH="20%"><b>Arguments:</b></td>

<td WIDTH="80%"></td>
</tr>

<tr>
<td VALIGN=TOP><i>&nbsp;&nbsp;&nbsp; zz</i></td>

<td>Pointer to the Zoltan structure, created by <b><a href="ug_interface_init.html#Zoltan_Create">Zoltan_Create</a></b>,
which has been used in the ordering routine.</td>
</tr>

<tr>
<td><b>Returned Value:</b></td>

<td></td>
</tr>

<tr>
<td VALIGN=TOP>&nbsp;&nbsp;&nbsp; int</td>

<td>The number of leaves in the elimination tree.</td>
</tr>
</table>

<p>

<!------------------------------------------------------------------------->


<!------------------------------------------------------------------------->
<hr WIDTH="100%"><a NAME="Zoltan_Order_Get_Block_Leaves"></a>
<hr WIDTH="100%">
<table WIDTH="100%" NOSAVE >
<tr NOSAVE>
<td VALIGN=TOP NOSAVE>C:</td>

<td WIDTH="85%">void <b>Zoltan_Order_Get_Block_Leaves</b> (
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;struct <b>Zoltan_Struct</b> *<i>zz</i>,
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;int *<i>leaves</i>)
</tr>

<tr NOSAVE>
<td VALIGN=TOP NOSAVE>C++:</td>

<td WIDTH="85%">void <b>Zoltan::Order_Get_Block_Leaves</b> (
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;struct <b>Zoltan_Struct</b> *<i>zz</i>,
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;int *<i>leaves</i>)
</tr>


</table>

<hr WIDTH="100%"><b>Zoltan_Order_Get_Block_Leaves </b> get the indices
of the blocks that are leaves in the elimination tree.
  <br>&nbsp;
<table WIDTH="100%" NOSAVE > <tr> <td VALIGN=TOP
WIDTH="20%"><b>Arguments:</b></td>

<td WIDTH="80%"></td>
</tr>

<tr>
<td VALIGN=TOP><i>&nbsp;&nbsp;&nbsp; zz</i></td>

<td>Pointer to the Zoltan structure, created by <b><a href="ug_interface_init.html#Zoltan_Create">Zoltan_Create</a></b>,
which has been used in the ordering routine.</td>
</tr>

<tr>
<td VALIGN=TOP><i>&nbsp;&nbsp;&nbsp; leaves</i></td>

<td>Array of indices of the blocks that are leaves in the elimination. The last element of this array is -1. The array must be of size <i>number of leave + 1</i> and must be allocated by the user before the call.</td>
</tr>


</table>

<p>

<!------------------------------------------------------------------------->





<hr WIDTH="100%">[<a href="ug.html">Table of Contents</a>&nbsp; | <a href="ug_interface_color.html">Next:&nbsp;
Coloring Functions</a>&nbsp; |&nbsp; <a href="ug_interface_mig.html">Previous:&nbsp;
Migration Functions</a>&nbsp; |&nbsp; <a href="https://www.sandia.gov/general/privacy-security/index.html">Privacy and Security</a>]
</body>
</html>
